In stark contrast to his form at Chelsea, the winger managed a solitary goal for Los Blancos and assisted 7 in all his appearances.
Benzema and Hazard were also key in Real Madrid's third goal, with the French striker picking out Fede Valverde at the back post after a counter attack.
Hazard has had a awful time with injuries since joining Madrid for 100 million euros ($113 million) from Chelsea in 2019 but the Belgian will hope his stunning strike from distance at the Alfredo di Stefano can kick-start his career in Spain.
His only previous goal for Zinedine Zidane's side came on October 5 a year ago.
The Belgian opened the scoring with a superb left-foot shot into the left corner from outside the penalty area and what a goal that was to break his duck.
He had missed the first seven games of the campaign before playing his first minutes since July on Tuesday as a late substitute in a 2-2 draw at Borussia Moenchengladbach in the Champions League.
"There was a discussion" between Benzema and Vinicius, Frenchman Zidane said. "Bit by bit he is getting back to his best". You could see the quality that he has linking up with other players.
This suggests Zidane needs all those players to be fresh for Inter, whilst Casemiro was withdrawn just 10 minutes later, again giving an indication that the Brazilian would start against Conte's charges. "We need to keep training and be ready".
"There is still a long way to go but we need to work hard to improve".